Generalized equivalent bandwidth defined by using Renyi's entropy and its estimation

In this paper, we present the definition of a the generalized equivalent bandwidth (EBW) of a stochastic process. The generalized EBW is defined by W ( α ) = exp( H ( α ) )/2, where H ( α ) is Renyi's entropy H ( α ) = 1/(1- α )log ( -infinity Integral infinity ) p α ( f ) df , p ( f ) is the normlized power spectrum and α greater than or equal to 0 is the order of the EWB. The generalized EBW is a new class of EBW which can represent major equivalent bandwidths uniformly. We also argue an interpretation of the generalized EBW from a different perspective. In latter of this article, we examine an estimation property of the generalized EBW. When we obtain an estimated smoothed power spectrum by using the convolution of periodogram and smoothing window, we evaluate how smoothing window length, data length or the variance of an estimated spectrum affect estimation of the generalized EBW. The result indicates that if we increase the data length while keeping the variance constant, the increase rate of the generalized EBW caused by smoothing window will decrease. On the other hand, if we decrease the variance while holding the data length fixed, the generalized EBW of estimated power spectrum will increase.